Problem: The equation of a circle $C$ is $x^2+y^2+16x-2y+16 = 0$. What is its center $(h, k)$ and its radius $r$ ?
To find the equation in standard form, complete the square. $(x^2+16x) + (y^2-2y) = -16$ $(x^2+16x+64) + (y^2-2y+1) = -16 + 64 + 1$ $(x+8)^{2} + (y-1)^{2} = 49 = 7^2$ Thus, $(h, k) = (-8, 1)$ and $r = 7$.